I can show you more than that

In a previous post, I talked about my grading system based on the mantra, "Show me what you can do." Here's a quick example of a student's response to a quiz item that shows why this proficiency-based approach feels so right:

One of my learning targets was:

___1.5. I can solve linear systems and represent the solution symbolically and graphically.

I stated that objective at the top of the quiz, along with several others, then gave the following task:

The solutions to the following system of equations are provided. Show that you can use the elimination and substitution methods (use each one once) to solve these problems.

{y = 3x+6
{2x + 4y = -4              solution is (-2,0)  

{7.5x - y = 10
{15x - 4y = 10            solution is (2,5)

I gave them the solutions because 1) the task wasn't really about correct answers, it was about applying particular methods and choosing between them; 2) they would need correct answers to attempt a subsequent task, and 3) because of an idea shared in this deltascape post.

One student's response struck me as worthy of sharing here. I'll summarize:

He basically solved both tasks correctly, carefully noting with a small (S) and (E) the method he would be using on each task, and then without prompting he squeezed in a small but accurate graph of the second system of lines and labeled the point of intersection on the graph.

I hadn't asked him to sketch a graph. I hadn't really even provided room for it. Why did he graph it? Then it hit me: the learning target refers to solving symbolically and graphically. I had only requested the symbolic solution method, but he knew he could do both, so he took the time to show me.

When you ask students to "show you what they can do," you might be pleasantly surprised with just how much they can share.